Average Error: 0.0 → 0.0
Time: 13.2s
Precision: 64
\[\frac{2.307529999999999859028321225196123123169 + x \cdot 0.2706100000000000171951342053944244980812}{1 + x \cdot \left(0.992290000000000005364597654988756403327 + x \cdot 0.04481000000000000260680366181986755691469\right)} - x\]
↓
\[\frac{2.307529999999999859028321225196123123169 + x \cdot 0.2706100000000000171951342053944244980812}{1 + \left(0.04481000000000000260680366181986755691469 \cdot {x}^{2} + 0.992290000000000005364597654988756403327 \cdot x\right)} - x\]
\frac{2.307529999999999859028321225196123123169 + x \cdot 0.2706100000000000171951342053944244980812}{1 + x \cdot \left(0.992290000000000005364597654988756403327 + x \cdot 0.04481000000000000260680366181986755691469\right)} - x
↓
\frac{2.307529999999999859028321225196123123169 + x \cdot 0.2706100000000000171951342053944244980812}{1 + \left(0.04481000000000000260680366181986755691469 \cdot {x}^{2} + 0.992290000000000005364597654988756403327 \cdot x\right)} - x
double f(double x) {
        double r75617 = 2.30753;
        double r75618 = x;
        double r75619 = 0.27061;
        double r75620 = r75618 * r75619;
        double r75621 = r75617 + r75620;
        double r75622 = 1.0;
        double r75623 = 0.99229;
        double r75624 = 0.04481;
        double r75625 = r75618 * r75624;
        double r75626 = r75623 + r75625;
        double r75627 = r75618 * r75626;
        double r75628 = r75622 + r75627;
        double r75629 = r75621 / r75628;
        double r75630 = r75629 - r75618;
        return r75630;
}
↓
double f(double x) {
        double r75631 = 2.30753;
        double r75632 = x;
        double r75633 = 0.27061;
        double r75634 = r75632 * r75633;
        double r75635 = r75631 + r75634;
        double r75636 = 1.0;
        double r75637 = 0.04481;
        double r75638 = 2.0;
        double r75639 = pow(r75632, r75638);
        double r75640 = r75637 * r75639;
        double r75641 = 0.99229;
        double r75642 = r75641 * r75632;
        double r75643 = r75640 + r75642;
        double r75644 = r75636 + r75643;
        double r75645 = r75635 / r75644;
        double r75646 = r75645 - r75632;
        return r75646;
}

Error

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.0

    \[\frac{2.307529999999999859028321225196123123169 + x \cdot 0.2706100000000000171951342053944244980812}{1 + x \cdot \left(0.992290000000000005364597654988756403327 + x \cdot 0.04481000000000000260680366181986755691469\right)} - x\]

  2. Taylor expanded around 0 0.0

    \[\leadsto \frac{2.307529999999999859028321225196123123169 + x \cdot 0.2706100000000000171951342053944244980812}{1 + \color{blue}{\left(0.04481000000000000260680366181986755691469 \cdot {x}^{2} + 0.992290000000000005364597654988756403327 \cdot x\right)}} - x\]

  3. Final simplification0.0

    \[\leadsto \frac{2.307529999999999859028321225196123123169 + x \cdot 0.2706100000000000171951342053944244980812}{1 + \left(0.04481000000000000260680366181986755691469 \cdot {x}^{2} + 0.992290000000000005364597654988756403327 \cdot x\right)} - x\]

Reproduce

herbie shell --seed 2019235 
(FPCore (x)
  :name "Numeric.SpecFunctions:invIncompleteGamma from math-functions-0.1.5.2, C"
  :precision binary64
  (- (/ (+ 2.30753 (* x 0.27061000000000002)) (+ 1 (* x (+ 0.992290000000000005 (* x 0.044810000000000003))))) x))